Finite Group Databasebeta

← #25134158

Subgroups — #25134158

Order 11008.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583133C211yesmaximal, characteristic, complemented
2C2×#14583033C211yesmaximal, characteristic, complemented
3C2×#14583033C211yesmaximal, characteristic, complemented
4C22×#13063246C211yesmaximal, characteristic, complemented
5#19138035C211yesmaximal, characteristic, complemented
6#19135826C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135666C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×D42×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic, complemented
18C22×#10621882C2211yescharacteristic, complemented
19C23×C43⋊C8C2211yescharacteristic, complemented
20C2×#13063299C2211yescharacteristic, complemented
21C2×#13063299C2211yescharacteristic, complemented
22C2×#13063297—21no—
23C22×C4⋊Dic43C2211yescharacteristic, complemented
24#14583133—24no—
25#14583033—24no—
26#14583033—24no—
27C2×#13063258C2211yescharacteristic, complemented
28C2×#13063246—24no—
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic, complemented
33C2×#13063246C2211yescharacteristic, complemented
34C2×#13063246C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic, complemented
36C2×#13063246C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic, complemented
38C2×#13063245C2211yescharacteristic, complemented
39C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42#14582821—21no—
43#14582815—21no—
44#14582801C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582776—21no—
47#14582759C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C23×D4×C43—21no—
53C23×D4×C43C2211yescharacteristic
54C23×D4×C43C2211yescharacteristic
55D42×C43—24no—
56D42×C43—24no—
57C2×#127×C43C2211yescharacteristic
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×#120×C43—21no—
63C2×C4×D4×C43C2211yescharacteristic
64C2×C4×D4×C43C2211yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C23×Dic43—21no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—41no—
76C2×#10621882—41no—
77C2×#10621882—41no—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063299—22no—
86#13063299—22no—
87#13063299—22no—
88#13063299—41no—
89#13063297—44no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102#13063258—22no—
103#13063246—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246—41no—
111#13063246D414yescomplemented
112#13063245—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—22no—
115C22⋊(C43⋊C8)—41no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C25×C43—21no—
119C25×C43—21no—
120C22×D4×C43—22no—
121C22×D4×C43—22no—
122C22×D4×C43—28no—
123C22×D4×C43—21no—
124C22×D4×C43—21no—
125C22×D4×C43—22no—
126C22×D4×C43—22no—
127C22×D4×C43—22no—
128C22×D4×C43—22no—
129C22×D4×C43—21no—
130C22×D4×C43—21no—
131C22×D4×C43—21no—
132C22×D4×C43—22no—
133C22×D4×C43—21no—
134C22×D4×C43—41no—
135C22×D4×C43—41no—
136C22×D4×C43—41no—
137C22×D4×C43—41no—
138C22×D4×C43—44no—
139C22×D4×C43—44no—
140C22×D4×C43D411yescharacteristic
141C22×D4×C43D414yescomplemented
142C22×D4×C43C2311yescharacteristic
143C22×D4×C43C2311yescharacteristic
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148#127×C43—22no—
149#127×C43—22no—
150#121×C43—28no—
151#121×C43—22no—
152#121×C43—22no—
153#121×C43—22no—
154#121×C43D414yescomplemented
155#120×C43—28no—
156#120×C43—28no—
157C4×D4×C43—22no—
158C4×D4×C43—22no—
159C4×D4×C43—22no—
160C4×D4×C43—22no—
161C2×C4⋊C4×C43D411yescharacteristic
162C2×C4⋊C4×C43C2311yescharacteristic
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43—21no—
165C2×C22⋊C4×C43—21no—
166C2×C22⋊C4×C43D411yescharacteristic
167C2×C22⋊C4×C43D411yescharacteristic
168C2×C42×C43C2311yescharacteristic
169C24×C43—21no—
170C24×C43—24no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—24no—
174C24×C43—42no—
175C24×C43—42no—
176C24×C43—42no—
177C24×C43—42no—
178C24×C43—42no—
179C24×C43—42no—
180C24×C43—42no—
181C24×C43—42no—
182C24×C43—81no—
183C24×C43—81no—
184C24×C43—81no—
185C24×C43—81no—
186C24×C43C2×D411yescharacteristic
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—24no—
193C2×D4×C43—24no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—22no—
200C2×D4×C43—24no—
201C2×D4×C43—22no—
202C2×D4×C43—28no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—44no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—42no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—432no—
224C2×D4×C43—44no—
225C2×D4×C43—42no—
226C2×D4×C43—42no—
227C2×D4×C43—42no—
228C2×D4×C43—42no—
229C2×D4×C43—81no—
230C2×D4×C43—81no—
231C2×D4×C43D814yescomplemented
232C2×D4×C43C2×D412yes—
233C2×D4×C43C2×D412yes—
234C2×D4×C43C2×D412yes—
235C2×D4×C43C2×D412yes—
236C2×D4×C43#4112yes—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—24no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—42no—
250C22×C4×C43—42no—
251C22×C4×C43C2×D412yes—
252C22×C4×C43C2×D412yes—
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43C2411yescharacteristic
258C2×C22⋊D43—42no—
259C2×C22⋊D43—42no—
260C2×C22⋊D43—42no—
261C2×C22⋊D43—42no—
262C2×C22⋊D43—42no—
263C2×C22⋊D43—81no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—42no—
268C22×Dic43—42no—
269C22×Dic43—81no—
270C2×D172—21no—
271C2×D172—21no—
272C2×D172—21no—
273C2×D172—21no—
274C2×D172—21no—
275C2×D172—21no—
276C4⋊C4×C43—22no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43C2×D412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C22⋊C4×C43—24no—
282C22⋊C4×C43—22no—
283C22⋊C4×C43—22no—
284C42×C43—21no—
285C42×C43—21no—
286C22⋊Dic43—42no—
287#10621882—44no—
288#10621882—44no—
289#10621882—44no—
290(C2×D43)⋊C4—42no—
291(C2×D43)⋊C4—42no—
292(C2×D43)⋊C4—42no—
293(C2×D43)⋊C4—81no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—42no—
300C4⋊Dic43C2×D412yescomplemented
301Dic43⋊C4—42no—
302C2×C43⋊C8—21no—
303C2×C43⋊C8—21no—
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8—21no—
307C2×C43⋊C8—21no—
308C2×C43⋊C8—21no—
309C2×C43⋊C8—21no—
310C2×C43⋊C8—21no—
311C2×C43⋊C8—21no—
312C2×C43⋊C8—21no—
313C2×C43⋊C8—44no—
314C2×C43⋊C8C2×D412yescomplemented
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—22no—
321C23×C43—21no—
322C23×C43—22no—
323C23×C43—21no—
324C23×C43—22no—
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—48no—
331C23×C43—48no—
332C23×C43—48no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—48no—
350C23×C43—84no—
351C23×C43—84no—
352C23×C43—84no—
353C23×C43—84no—
354C23×C43—84no—
355C23×C43—84no—
356C23×C43—84no—
357C23×C43—84no—
358C23×C43—84no—
359C23×C43—84no—
360C23×C43#12012yes—
361C23×C43C2×D812yes—
362C23×C43C2×D812yes—
363C23×C43AGL(1,ℤ/8)12yes—
364C23×C43C22×D411yescharacteristic
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372D4×C43—28no—
373D4×C43—22no—
374D4×C43—22no—
375D4×C43—22no—
376D4×C43—22no—
377D4×C43—22no—
378D4×C43—22no—
379D4×C43—22no—
380D4×C43—48no—
381D4×C43—48no—
382D4×C43—48no—
383D4×C43—48no—
384D4×C43—48no—
385D4×C43—41no—
386D4×C43—41no—
387D4×C43—41no—
388D4×C43—41no—
389D4×C43—84no—
390D4×C43#12114yescomplemented
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—22no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—21no—
406C2×C4×C43—48no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43#12012yes—
414C2×C4×C43C2×D812yes—
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C2×#4111yescharacteristic
419C2×C4×C43H(5,𝔽2)11yescharacteristic
420C2×C4×C43H(5,𝔽2)11yescharacteristic
421C22⋊D43—84no—
422C22⋊D43—84no—
423C2×Dic43—22no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—84no—
433D172—41no—
434D172—41no—
435D172—41no—
436D172—41no—
437C43⋊C8—22no—
438C43⋊C8—41no—
439C43⋊C8—41no—
440C43⋊C8—41no—
441#24424—431nomaximal, Sylow
442C22×C43—22no—
443C22×C43—22no—
444C22×C43—22no—
445C22×C43—22no—
446C22×C43—22no—
447C22×C43—22no—
448C22×C43—24no—
449C22×C43—22no—
450C22×C43—22no—
451C22×C43—22no—
452C22×C43—41no—
453C22×C43—42no—
454C22×C43—41no—
455C22×C43—42no—
456C22×C43—41no—
457C22×C43—42no—
458C22×C43—42no—
459C22×C43—42no—
460C22×C43—41no—
461C22×C43—42no—
462C22×C43—42no—
463C22×C43—42no—
464C22×C43—42no—
465C22×C43—42no—
466C22×C43—42no—
467C22×C43—42no—
468C22×C43—816no—
469C22×C43—816no—
470C22×C43—81no—
471C22×C43—81no—
472C22×C43—81no—
473C22×C43—81no—
474C22×C43—81no—
475C22×C43—81no—
476C22×C43—81no—
477C22×C43—81no—
478C22×C43#44714yescomplemented
479C22×C43C2×#12011yescharacteristic
480C22×C43D4211yescharacteristic
481C22×C43#54611yescharacteristic
482C22×C43C22×D811yescharacteristic
483C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
484C22×C43#57611yescharacteristic
485C22×C43#57711yescharacteristic
486C2×D43—81no—
487C2×D43—81no—
488C2×D43—81no—
489C2×D43—81no—
490C2×D43—81no—
491C2×D43—81no—
492C2×D43—81no—
493C4×C43—22no—
494C4×C43—22no—
495C4×C43—41no—
496C4×C43—42no—
497C4×C43—41no—
498C4×C43C2×#12111yescharacteristic
499C4×C43#53411yescharacteristic
500C4×C43D4211yescharacteristic
501C4×C43#54611yescharacteristic
502Dic43—42no—
503Dic43—81no—
504Dic43—81no—
505C2×D42D4311yescharacteristic, complemented
506C2×#466—431no—
507C2×#447—431no—
508C2×#447—431no—
509C22×#102—431no—
510#2416—431no—
511#2041—431no—
512#2033—431no—
513#2011—431no—
514#1999—431no—
515#1879—431no—
516#1874—431no—
517#1869—431no—
518#1862—431no—
519#1786—431no—
520C2×C43—24no—
521C2×C43—42no—
522C2×C43—44no—
523C2×C43—82no—
524C2×C43—82no—
525C2×C43#241011yescharacteristic
526C2×C43C2×#44711yescharacteristic
527C2×C43#301211yescharacteristic
528C2×C43#326511yescharacteristic
529C2×C43D4×D811yescharacteristic
530C2×C43#329411yescharacteristic
531C2×C43#331811yescharacteristic
532D43—161no—
533C23×D4—21no—
534C23×D4C2×D4311yescharacteristic
535C23×D4C2×D4311yescharacteristic
536C22×D8—431no—
537C22×D8—431no—
538C22×D8—431no—
539C23×C8—431no—
540D42—24no—
541D42—24no—
542C2×#127C2×D4311yescharacteristic
543C2×#121—21no—
544C2×#121—431no—
545C2×#121—431no—
546C2×#121—861no—
547C2×#121C2×D4311yescharacteristic
548C2×#121C2×D4311yescharacteristic
549C2×#120—21no—
550C2×#120—21no—
551C2×C4×D4C2×D4311yescharacteristic
552C2×C4×D4C2×D4311yescharacteristic
553C22×C4⋊C4—431no—
554#466—864no—
555#447—864no—
556#447—864no—
557C2×#107—431no—
558C2×#102—431no—
559C2×#102—431no—
560C2×#102—431no—
561C2×#102—431no—
562C2×#102—431no—
563C2×#102—431no—
564C2×#102—431no—
565C2×#102—431no—
566C2×#102—431no—
567C2×#102—431no—
568C2×#102—864no—
569C2×C22⋊C8—431no—
570C2×C22⋊C8—431no—
571C2×C22⋊C8—431no—
572#396—861no—
573#394—861no—
574#390—431no—
575#389—431no—
576#386—861no—
577#380—431no—
578#340—431no—
579#340—431no—
580#336—431no—
581#336—431no—
582C43#2442411yescharacteristic, complemented, Sylow
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—44no—
604C22×D4—44no—
605C22×D4—431no—
606C22×D4—861no—
607C22×D4—861no—
608C22×D4C22⋊D4311yescharacteristic
609C22×D4C22⋊D4314yescomplemented
610C22×D4C22×D4311yescharacteristic
611C22×D4C22×D4311yescharacteristic
612C22×D4C22×D4311yescharacteristic
613C23×C4—21no—
614C23×C4—861no—
615C23×C4C22×D4311yescharacteristic
616C23×C4C22×D4311yescharacteristic
617C2×D8—862no—
618C2×D8—862no—
619C2×D8—862no—
620C2×D8—862no—
621C2×D8—862no—
622C2×D8—862no—
623C2×D8—1721no—
624C2×D8—1721no—
625C2×D8—1721no—
626C22×C8—431no—
627C22×C8—431no—
628C22×C8—431no—
629C22×C8—431no—
630C22×C8—862no—
631C22×C8—862no—
632C22×C8—1721no—
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—862no—
640#121—862no—
641#121—862no—
642#121—1721no—
643#121—1724no—
644#121C22⋊D4314yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—431no—
652C2×C4⋊C4—431no—
653C2×C4⋊C4—431no—
654C2×C4⋊C4—862no—
655C2×C4⋊C4—861no—
656C2×C4⋊C4—861no—
657C2×C4⋊C4—1721no—
658C2×C4⋊C4C22⋊D4311yescharacteristic
659C2×C4⋊C4C22×D4311yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C22⋊C4—861no—
667C2×C22⋊C4—861no—
668C2×C22⋊C4C22⋊D4311yescharacteristic
669C2×C22⋊C4C22⋊D4311yescharacteristic
670C2×C42C22×D4311yescharacteristic
671#107—862no—
672#102—434no—
673#102—862no—
674#102—862no—
675#102—862no—
676#102—862no—
677#102—862no—
678#102—862no—
679#102—862no—
680#102—862no—
681#102—1721no—
682C22⋊C8—862no—
683C22⋊C8—862no—
684C22⋊C8—1721no—
685#95—861no—
686#95—861no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—81no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—861no—
705C24C2×C22⋊D4311yescharacteristic
706C24C2×C22⋊D4311yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—432no—
740C2×D4—44no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—861no—
750C2×D4—861no—
751C2×D4—861no—
752C2×D4—861no—
753C2×D4—861no—
754C2×D4—861no—
755C2×D4—3441no—
756C2×D4—1722no—
757C2×D4—1722no—
758C2×D4—1722no—
759C2×D4—1722no—
760C2×D4—1722no—
761C2×D4#1062188214yescomplemented
762C2×D4D4×D4312yes—
763C2×D4#1062190012yes—
764C2×D4C2×C22⋊D4312yes—
765C2×D4C2×C22⋊D4312yes—
766C2×D4C2×C22⋊D4312yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—3441no—
785C22×C4—1722no—
786C22×C4—1722no—
787C22×C4C2×C22⋊D4311yescharacteristic
788C22×C4C2×C22⋊D4311yescharacteristic
789C22×C4C2×C22⋊D4311yescharacteristic
790C22×C4C2×C22⋊D4312yes—
791C22×C4C2×C22⋊D4312yes—
792C22×C4C2×C22⋊D4311yescharacteristic
793C22×C4C23×D4311yescharacteristic
794D8—1724no—
795D8—1724no—
796D8—1724no—
797C2×C8—432no—
798C2×C8—861no—
799C2×C8—861no—
800C2×C8—861no—
801C2×C8—861no—
802C2×C8—861no—
803C2×C8—861no—
804C2×C8—861no—
805C2×C8—861no—
806C2×C8—861no—
807C2×C8—861no—
808C2×C8—861no—
809C2×C8—1724no—
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—432no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4—861no—
816C4⋊C4—861no—
817C4⋊C4—861no—
818C4⋊C4—1722no—
819C4⋊C4—1722no—
820C4⋊C4C2×C22⋊D4312yes—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—3441no—
827C22⋊C4—1722no—
828C22⋊C4—1722no—
829C22⋊C4—1722no—
830C22⋊C4—1722no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—48no—
868C23—84no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—1721no—
879C23—1721no—
880C23—1721no—
881C23—1721no—
882C23—1721no—
883C23—1721no—
884C23—1721no—
885C23#1306329412yes—
886C23C2×#1062188212yes—
887C23C2×#1062188212yes—
888C23#1306335112yes—
889C23C22×C22⋊D4311yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—84no—
908D4—3444no—
909D4—3444no—
910D4—1721no—
911D4—1721no—
912D4—1721no—
913D4—1721no—
914D4#1306329714yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—48no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—862no—
938C2×C4—3444no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1721no—
947C2×C4#1306329412yes—
948C2×C4C2×#1062188212yes—
949C2×C4C2×D4×D4311yescharacteristic
950C2×C4C22×C22⋊D4311yescharacteristic
951C2×C4C22×C22⋊D4311yescharacteristic
952C2×C4C2×#1062190011yescharacteristic
953C2×C4#1306337011yescharacteristic
954C2×C4#1306337011yescharacteristic
955C8—862no—
956C8—1721no—
957C8—1721no—
958C8—1721no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—24no—
969C22—42no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—3441no—
996C22—3441no—
997C22—3441no—
998C22—3441no—
999C22—3441no—
1000C22—3441no—
1001C22—3441no—
1002C22#1458303314yescomplemented
1003C22C2×#1306329411yescharacteristic
1004C22D4×C22⋊D4311yescharacteristic
1005C22#1458354311yescharacteristic
1006C22C22×#1062188211yescharacteristic
1007C22C2×#1306335111yescharacteristic
1008C22#1458370211yescharacteristic
1009C22#1458371011yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—42no—
1013C4—41no—
1014C4—41no—
1015C4—3441no—
1016C4—3441no—
1017C4—1722no—
1018C4C2×#1306329711yescharacteristic
1019C4#1458345811yescharacteristic
1020C4D4×C22⋊D4311yescharacteristic
1021C4#1458354311yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—6881no—
1028C2#1913796911yescharacteristic
1029C2C2×#1458303311yescharacteristic
1030C2#1914389911yescharacteristic
1031C2#1914608611yescharacteristic
1032C2D4×#1062188211yescharacteristic
1033C2#1914640811yescharacteristic
1034C2#1914673611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×D42×C43C2
socleC23×C43C22×D4
hypercenterC2×D42D43
hypocenterC43#24424
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583133C2semidirect
2. C2×#14583033C2semidirect
3. C2×#14583033C2semidirect
4. C22×#13063246C2semidirect
5. #19138035C2semidirect
6. #19135826C2semidirect
7. #19135774C2semidirect
8. #19135666C2semidirect
9. #19135591C2semidirect
10. #19134943C2semidirect
11. #19134913C2semidirect
12. #19134888C2semidirect
13. #19134842C2semidirect
14. #19134526C2semidirect
15. C2×D42×C43C2semidirect
17. C22×#10621882C22semidirect
18. C22×#10621882C22semidirect
19. C23×C43⋊C8C22semidirect
20. C2×#13063299C22semidirect
21. C2×#13063299C22semidirect
23. C22×C4⋊Dic43C22semidirect
27. C2×#13063258C22semidirect
32. C2×#13063246C22semidirect
33. C2×#13063246C22semidirect
34. C2×#13063246C22semidirect
35. C2×#13063246C22semidirect
36. C2×#13063246C22semidirect
37. C2×#13063246C22semidirect
38. C2×#13063245C22semidirect
39. C2×C22⋊(C43⋊C8)C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
44. #14582801C22semidirect
45. #14582797C22semidirect
47. #14582759C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
111. #13063246D4semidirect
141. C22×D4×C43D4semidirect
154. #121×C43D4semidirect
231. C2×D4×C43D8semidirect
300. C4⋊Dic43C2×D4semidirect
314. C2×C43⋊C8C2×D4semidirect
390. D4×C43#121semidirect
478. C22×C43#447semidirect
505. C2×D42D43semidirect
582. C43#24424semidirect
609. C22×D4C22⋊D43semidirect
644. #121C22⋊D43semidirect
761. C2×D4#10621882semidirect
914. D4#13063297semidirect
1002. C22#14583033semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145831332
C2×#145830332
C22×#130632462
#191380352
#191358262
#191357742
#191356662
#191355912
#191349432
#191349132
#191348882
#191348422
#191345262
C2×D42×C432
#2442443